Electric Force and Electric Field Practice Problems
PSI AP Physics 1
Name___________________________________
Multiple Choice
1. A plastic rod is rubbed with a piece of wool. During the process the plastic rod acquires a
negative charge and the wool:
(A) acquires an equal positive charge
(B) acquires an equal negative charge
(C) acquires less in magnitude positive charge
(D) acquires less in magnitude negative charge
2. A positively charged sphere is brought near one end of an uncharged metal bar. The end A and
B of the metal bar will be charged:
(A) positive, negative
(B) negative, positive
(C) positive, positive
(D) negative, negative
3. Sphere A carries a net positive charge, and sphere B is neutral. They are placed near each other
on an insulated table. Sphere B is briefly touched with a wire that is grounded. Which statement
is correct?
(A) sphere B remains neutral
(B) sphere B is now positively charged
(C) sphere B is now negatively charged
(D) sphere B is now positive and sphere A is negative
4.
An originally neutral electroscope is briefly touched with a negatively charged plastic rod. Which
statement is correct?
(A) electroscope remains neutral
(B) electroscope becomes negatively charged
(C) electroscope becomes positively charged.
(D) electroscope becomes negatively charged and rod becomes positively charged
1
Questions 5-6
5. An electric charge Q is placed at the origin. A charge q is placed at point B and the force on
charge q due to charge Q is F. What is the force on charge q if charge g is moved to point A?
(A) 4F
(B) 2F
(C) F/4
(D) F/2
6. An electric charge Q is placed at the origin. A charge q is placed at point A and the force on
charge q due to charge Q is F. What is the force on charge q if charge g is moved to point C?
(A) 9F
(B) 3F
(C) F/4
(D) F/3
7. A student in a physics lab wants to determine the type of an electric charge on initially charged
electroscope. He brings two charged rods without touching the electroscope. The positively
charged rod causes the leaves to move further apart and the negatively rod causes leaves to
move closer to each other. What type of the electric charge was initially on the electroscope?
(A) positive
(B) negative
(C) neutral
(D) couldn’t be determine because the electroscope wasn’t grounded
8.
Two charged objects with an equal charge of Q separated by a distance r attract each other with
a certain force. If the charges on both objects are doubled and the separation is halved, the force
between them is:
(A) 4 times greater
(C) 4 times less
(B) 2 times greater
(D) 16 times greater
2
9. Two identical conducting spheres are charged to +Q and -3Q and separated by a distance r. The
attractive force between the spheres is F. The two spheres are brought in a brief contact and then
moved to the original positions. If the new electrostatic force between the spheres is F’, which of
the following is true?
(A) F’ = F
(B) F’ = 3F
(C) F’ = 1/3 F
(D) F’ = 9F
Questions 10-11
Three positive charges with an equal charge of Q are located at the corners of an equilateral
triangle of side r.
10. What is the direction of the net force on charge C due to charges A and B?
(A)
(B)
(C)
(D)
11. What is the magnitude of the net force on charge C due to two charges A and B?
3
Questions 12-13
Three equal in magnitude charges are located at the corners of an equilateral triangle of side r.
The charges A and C are positive and charge B is negative.
12. What is the direction of the net force on charge C due to charges A and B?
(A)
(B)
(C)
(D)
13. What is the magnitude of the net force on charge C due to charges A and B?
14. Four positive Q charges are arranged in the corner of a square as shown on the diagram. What is
the direction of the net force on the test charge q placed at the center of the square?
(A)
(B)
(C)
(D) the net force is zero
4
15. Four Q charges are arranged in the corner of a square as shown on the diagram. What is the
direction of the net force on the test charge q placed at the center of the square?
(A)
(B)
(C)
(D)
16. Four Q charges are arranged in the corner of a square as shown on the diagram. What is the
magnitude of the net force on the test charge q placed at the center of the square?
(A)
(B)
(C)
(D)
17. An electric charge Q is placed at the origin. If the magnitude of the electric field at point A is E,
what is the electric field at point B?
(A) 4E
(B) 2E
(C) E/4
(D) E/2
5
18. A conducting sphere is charged with a negative charge –Q. Which statement about the charge
distribution is correct?
(A)
(B)
(C)
(D)
Charge is concentrated at the center of the sphere
Charge is concentrated at the bottom part of the sphere
Charge is evenly distributed throughout the volume of the sphere
Charge is evenly distributed on the surface of the sphere
19. The conducting sphere shown above is charged with a negative charge –Q. Which statement
about the magnitude electric field of the sphere is correct?
(A) Maximum at the center
(D) Maximum at point 4 m
(B) Maximum at point 1 m
(C) Maximum at point 3 m
20. Two parallel conducting plates are charged with an equal and opposite charges. Which statement
is true about the direction of the electric field?
(A) Directed in +X (B) Directed +Y (C) Directed in -X (D) Directed in -Y
21. Two parallel conducting plates are charged with an equal and opposite charges. Which statement
is true about the magnitude of the electric field?
(A) Greater at point A
(B) Greater at point B
(C) Greater at point C
(D) The same at points B, C, D and zero at point A
6
22. A conducting sphere with a radius R is placed in a uniform electric field produced by two parallel
plates M and L. Which statement is true about the electric field inside the sphere?
(A)
(B)
(C)
(D)
Increasing from the center to the surface
Decreasing from the center to the surface
Increasing from the left to the right across the sphere
Is zero everywhere inside the sphere
Questions 23-24
An electron with a charge e and mass m is accelerated from rest for a time T by a uniform electric
field that exerts a force F on the electron.
23. What is the magnitude of the electric field?
(A) eF
(B) F/m
(C) F/e
(D) em/F
24. The speed of the electron after it has accelerated for the time T is most nearly
(A) eT/m
(B) FT/m
(C) emT/F
(D) FT/em
25. Two isolated charges, + 2q and -5q, are 2 centimeters apart. If F is the magnitude of the force
acting on charge -5Q, what are the magnitude and direction of the force acting on charge + 2q ?
Magnitude
(A)
(1/2) F
(B)
2F
(C)
F
(D)
F
Direction
Toward charge -5q
Away from charge -5q
Toward charge -5q
Away from charge -5q
7
26. Which of the following is true about the net force on an uncharged conducting sphere in a nonuniform electric field?
(A) It is zero
(B) It is in the direction of the field
(C) It is in the direction opposite to the field
(D) It produces a torque on the sphere about the direction of the field
27. Two negative charges A and B are placed at the corners of equilateral triangle. What is the
direction of the net electric field at point C?
(A)
(B)
(C)
(D)
28. Two negative charges A and B are placed at the corners of equilateral triangle. What is the
magnitude of the net electric field at point C?
(A)
(B)
(C)
(D)
8
Questions 29-30
The figure above shows two particles, each with a charge of -Q, that are located at the opposite
corners of a square of side d.
29. What is the direction of the net electric field at point P?
(A)
(B)
(C)
(D)
30. What is the net electric field at point P?
(A)
(B)
(C)
(D)
31. A point charge Q1 = +4.0 µC is placed at point -2 m. A second charge Q2 is placed at point +3 m.
The net electric field at the origin is zero. What is charge Q 2?
Magnitude
(A)
9.0 µC
(B)
6.0 µC
(C)
3.0 µC
(D)
9.0 µC
Sign
(A) Positive
(B) Positive
(C) Positive
(D) Negative
9
32. A small sphere with charge q and mass m is attached to one end of an insulating string of length
L. The other end is attached to negatively charged wall. The electric field E due to the charged
wall is constant in the vicinity of the charged sphere. The string makes a constant angle ϴ with
the vertical. What is the sign and magnitude of charge q?
(A) Positive and magnitude
(B) Positive and magnitude
(C) Negative and magnitude
(D) Negative and magnitude
10
Multi-correct Section: For each question or incomplete statement, two of the answers are correct. For
each questions you must select both answers.
33. Two electrons are separated by a distance r. Which of the following statements is correct?
(A) There is an attractive electrostatic force between the electrons
(B) There is a repulsive electrostatic force between the electrons
(C) The gravitational force between the electrons much greater than electrostatic force
(D) The electrostatic force is much greater that gravitational force
34. A positively charged sphere of charge +Q is held stationary. A small test charge +q is placed near
the sphere and released from rest. The test charge will move away from the sphere with
(A) Increasing acceleration
(B) Decreasing acceleration
(C) Increasing velocity
(D) Decreasing velocity
35. Which of the following statement is true about a positively charge conductor?
(A) The electric field inside increases linearly from the center
(B) The electric field inside is zero
(C) The electric field lines are parallel to the surface of the conductor
(D) The electric filed lines are perpendicular to the surface of the conductor
11
36. A neutral conducting sphere A is placed on an insulating table. Which of the following will cause
the sphere to gain positive charge?
(A) Touch the sphere with a negatively charged rod
(B) Touch the sphere with a positively charged rod
(C) Bring a negatively charged rod near the sphere and briefly touch the sphere with a grounding
wire
(D) Bring a positively charged rod near the sphere and briefly touch the sphere with a grounding
wire
12
Chapter Questions
Electric Charge
Classwork
1. What happens to a plastic rod when it is rubbed with a piece of animal fur? What happens to the
piece of fur?
2. How many types of electric charge are there? What are they named?
3. How can you tell when two objects, after being rubbed together, have each acquired an electric
charge? How will the magnitude of the charge on each compare with one another? How about the
sign of the charge on each?
4. What happens when two glass rods are rubbed with silk and they are brought close to each other?
Homework
5. What happens between a plastic rod rubbed with a piece of animal fur and a glass rod rubbed with a
piece of silk when they are brought close to each other?
6. What happens when two glass rods are rubbed with silk and they are brought close to each other?
7. Who assigned the convention of the charge remaining on a glass rod after being rubbed by silk as
negative?
Atomic Structure and Source of Charge
Classwork
8. Which particle of an atom carries a positive charge? Which carries the negative charge?
9. When a neutral atom captures a free electron, what is the net charge on the atom? What do we call
this type of atom?
10. What is most of the atom composed of?
11. Is it possible to add 0.5e of charge to an object? Explain.
Homework
13
12. Eight electrons orbit a neutral oxygen atom. How many protons are in the nucleus?
13. When an electron is removed from a neutral atom, what is the net charge on the atom? What is this
type of atom called?
14. A glass rod obtains a positive charge after being rubbed by silk. Is this due to the glass gaining
protons, or losing electrons? Explain.
15. Describe two ways that you can give an electroscope a positive charge.
Conduction and Induction; Electroscope
Classwork
16. A student has a positively charged glass rod but she wants to charge an electroscope negatively.
What should she do to accomplish that? Why does that work?
17. A student brings a negatively charged plastic rod near a tiny piece of paper that is resting on a
tabletop. Will the paper be attracted or repelled? Explain why.
18. Why is it that when you take off a sweater in a dark room you can see tiny sparks and hear a
crackling sound?
Homework
19. A positively charged rod attracts a metal ball suspended at the end on an insulating string. Explain
the mechanism of attraction.
20. An electroscope (insulated from ground) is charged negatively and a charged rod is brought very
close but does not touch the electroscope. As a result the leaves move further apart. What kind of
electric charge is on the rod?
21. Two light paper strips are suspended at the ends of two insulating strings, and are far apart from each
other. One paper strip is charged and the other is not charged. Design an experiment to determine
which strip is charged.
22. A student touches an electroscope with his hand at the same time he brings a positively charged rod
close to the electroscope without touching. When he removes his hand first and then moves the rod
away from the electroscope the leaves move apart. Why? What type of charge is on the leaves?
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Electric Force (Coulomb’s Law)
Classwork
23. Will two charged objects interact on the Moon, where there is no atmosphere?
24. If the distance between two charged objects is doubled, what happens to the electrical force between
them?
25. When performing calculations using Coulomb’s Law, why is the force of gravity usually neglected?
Homework
26. Two charges repel each other with a force of F0. One of the charges is replaced with another charge
that is three times its magnitude. What is the new force between these charges in terms of F0?
27. Compare and contrast Coulomb’s Law with Newton’s Law of Universal Gravitation.
28. Does the mass of a charged object affect the electrical force between it and another charged object?
Electric Field
Classwork
29. What is the definition of the Electric Field and what equation was used to derive this concept?
30. Why can Electric Field lines never cross or touch each other? Do Electric Field lines exist?
31. Draw the electric field lines around a positive charge. How would these lines be different if the
charge was negative?
32. What is the significance of the density of the electric field lines about a charge?
Homework
33. Compare and contrast the Gravitational Field and the Electric Field.
34. What is the dominant field that acts on two electrons that are 10-12 m apart? Gravitational or
Electric Field?
35. How is the Electric Field due to several charges calculated?
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Chapter Problems
Coulomb’s Law
Classwork
(Use k = 9x109 Nm2/C2)
1. Two positive charges of 1 mC and 10 mC are separated by a distance of 10 m. Find the direction
and the magnitude of electrostatic force between the charges. Describe the direction in terms of “the
charges attract each other,” or “the charges repel each other.”
2. A particle with a charge of +7.4 μC is separated from another charged particle with a charge of –3.6
μC by a distance of 1.4 m. Find the direction and the magnitude of electrostatic force between the
particles.
3. A +1.4 nC charge exerts a repulsive force of 20.0 mN on a second charge which is located a
distance of 2.2 m away from it. What is the magnitude and sign of the second charge?
4. Two spherical objects, whose centers are 8.0 cm apart, have equal negative charges and repel each
other with a force of 9.0 mN. What is the charge on each of them? How many extra electrons are on
each of them?
5. Two conducting spheres have net charges of +9.00 μC and -7.00 μC and attract each other with a
force of 4.00 mN. The spheres are brought in contact and then moved apart to the initial distance.
What is the new force between the spheres? Is this force attractive or repulsive?
Homework
6. Two negative charges of 2.5 μC and 9.0 μC are separated by a distance of 25 cm. Find the direction
(in terms of repulsive or attractive) and the magnitude of the electrostatic force between the charges.
7. Two charges of +2.6 μC and –5.4 μC experience an attractive force of 6.5 mN. What is the
separation between the charges?
8. What is the distance between two charges, +7.8 μC and +9.2 μC, if they exert a force of 4.5 mN on
each other?
9. A –4.2 μC charge exerts an attractive force of 1.8 mN on a second charge which is a distance of 2.4
m away. What is the magnitude and sign of the second charge?
10. Two equal negative point charges repel each other with a force of 18.0 mN. What is the charge on
each object if the distance between them is 9.00 cm? How many extra electrons are on each object?
16
11. Two charged conducting spheres have net charges of +4.0 μC and -8.0 μC and attract each other
with a force of 16 mN. The spheres are brought into contact and then moved apart to the initial
distance. What is the new force between the spheres? Is this force attractive or repulsive?
12. What is the ratio of the electrostatic force to the gravitational force between two electrons?
I.
Electric Field
Classwork
13. A 2.40 μC charge is subject to a 3.00 mN force due to an Electric Field. What is the magnitude of
the Electric Field at the location of the charge?
14. A 6.3 μC electric charge is placed in an Electric Field with a magnitude of 5.0 x 105 N/C. What is the
electric force on the charge due to the Electric Field?
15. A 5.6 nC electric charge is placed in an Electric Field and experiences a force of 7.4 μN. What is the
magnitude of the Electric Field at that location?
Homework
16. What is the direction and magnitude of the Electric Field due to a -6.8 μC point charge at a distance
of 7.4 m?
17. An oil drop is charged negatively. How much charge is on the drop if the Electric Field is 6,400 N/C
at a distance of 1.2 m?
18. What is the direction and magnitude of the Electric Field 4.0 m away from an 8.6 μC charge?
19. The Electric Field due to a charged particle is 3,600 N/C at a location 2.4 m away from the particle.
How much electric charge is on the particle?
Electric Field relationship to Gravitational Field
Classwork
20. Calculate and compare the gravitational force and the electrical force between two protons that
are separated by 1.2 x 10-15 m (G = 6.67 x 10-11 Nm2/kg2, e = 1.60 x 10-19 C, mp = 1.67 x 10-27 kg).
21. Calculate and compare the gravitational force and the electrical force between two electrons that
are separated by 4.15 x 10-12 m (G = 6.67 x 10-11 Nm2/kg2, e = 1.60 x 10-19 C, me = 9.11 x 10-31 kg).
22. What is the magnitude of the Electric Field required to “levitate” an electron in the Earth’s
gravitational field.
17
Homework
23. Calculate and compare the gravitational force and the electrical force between two protons that
are separated by 4.25x 10-15 m (G = 6.67 x 10-11 Nm2/kg2, e = 1.60 x 10-19 C, mp = 1.67 x 10-27 kg).
24. Calculate and compare the gravitational force and the electrical force between two electrons that
are separated by 9.45 x 10-12 m (G = 6.67 x 10-11 Nm2/kg2, e = 1.60 x 10-19 C, me = 9.11 x 10-31 kg).
25. What is the magnitude of the Electric Field required to suspend an oil drop of mass 1.0 x 10-4 kg
with a charge of 6.2 x 10-6 C in the Earth’s gravitational field?
Electric Field of Multiple Charges
Classwork
26. Draw the Electric Field line surrounding one single positive charge.
27. Draw the Electric Field lines surrounding two positive electric charges that are in a horizontal line,
separated by a distance, r.
28. Draw the Electric Field lines surrounding a positive charge on the top and a negative charge below.
Homework
29. Draw the Electric Field line surrounding one single negative charge.
30. Draw the Electric Field lines surrounding two negative electric charges that are in a horizontal line,
separated by a distance, r.
31. Draw the Electric Field lines surrounding a negative charge on the left and a positive charge on the
right.
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The Net Electric Field
Classwork
+Q1
-3
+Q2
-2
-1
0
1
2
3
4
5
6
7
8
x(m)
32. As shown in the above diagram, a positive charge, Q1 = 2.6 μC, is located at a point, x1 = -3.0 m, and
a positive charge, Q2 = 1.4 μC, is located at a point, x2 = +4.0 m.
a. Find the magnitude and direction of the Electric Field at the origin due to charge Q1.
b. Find the magnitude and direction of the Electric Field at the origin due to charge Q2.
c. Find the magnitude and direction of the net Electric Field at the origin.
33. A positive charge, Q1 = 7.4 μC, is located at x1 = -2.0 m, a negative charge Q2 = -9.7 μC is located at a
point x2 = 3.0 m and a positive charge Q3 = 2.1 μC is located at a point x3 = 9.0 m.
a. Find the magnitude and direction of the Electric Field at the origin due to Q1.
b. Find the magnitude and direction of the Electric Field at the origin due to Q2.
c. Find the magnitude and direction of the Electric Field at the origin due to Q3.
d. Find the magnitude and direction of the net Electric Field at the origin.
Homework
-Q1
-3
-2
+Q2
-1
0
1
2
3
4
5
6
7
8
x(m)
34. As shown in the above diagram, a charge, Q1 = -3.6 μC, is located at a point, x1 = -2.0 m, and a
positive charge, Q2 = 2.8 μC, is located at a point, x2 = +6.0 m.
a. Find the magnitude and direction of the Electric Field at the origin due to charge Q1.
b. Find the magnitude and direction of the Electric Field at the origin due to charge Q2.
c. Find the magnitude and direction of the net Electric Field at the origin.
19
35. A positive charge, Q1 = 5.2 μC, is located at x1 = -2.0 m, a negative charge Q2 = -9.7 μC is located at a
point x2 = 4.0 m and a negative charge Q3 = -4.1 μC is located at a point x3 = 9.0 m.
a.
b.
c.
d.
Find the magnitude and direction of the Electric Field at the origin due to Q1.
Find the magnitude and direction of the Electric Field at the origin due to Q2.
Find the magnitude and direction of the Electric Field at the origin due to Q3.
Find the magnitude and direction of the net Electric Field at the origin.
20
Free Response Problems
1. Sphere 1 carries a positive charge Q =
+6 µC and located at the origin.
a. What is the direction of the electric
field at point P 0.6 m away from the
origin?
b. What is the magnitude of the
electric field at point P?
A test charge q = +1 µC and mass m = 2.5 g is
brought from infinity and placed at point P
c.
What is the direction of the electric
force on charge q due to charge Q?
d. What is the magnitude of the electric force on charge q due to charge Q?
e. What is the acceleration of charge q at the instant when it is released from point P?
2. A negatively charged sphere with charge Q = -20 µC is placed on
an insulating table a tiny charge q and mass of m = 3.6 g is
suspended at rest above charge Q. The distance between the
charges is 0.8 m.
a. What is the direction of the electric field due to charge Q at the
distance d above charge Q?
b. What is the magnitude of the electric field due to charge Q at
the distance d above charge Q?
c.
On the diagram below show all the forces applied on charge q.
d. What should be the sign and magnitude of the charge q in order to keep it at equilibrium?
21
3. A charge Q1 = -32 µC is fixed on the y axis at y = 4 m, and a charge Q 2 = +18 µC is fixed on the x
axis at x = 3 m.
a. Calculate the magnitude of the electric field E1 at the origin due to charge Q1.
b. Calculate the magnitude of the electric field E2 at the origin due to charge Q2.
c.
On the diagram below, draw and label the electric fields E1, E2 and the net electric field at the
origin.
d. Calculate the net electric field at the origin due to two charges Q 1 and Q2.
22
4. A wall has a negative charge distribution producing a uniform field. A small dielectric sphere of
mass 10 g and charge of -90 µC is attached to one end of insulating string 0.6 m long. The other
end of the string is attached to the wall. The uniform electric field has a magnitude of 500 N/C.
a. What is the direction of the uniform electric field?
b. What is the direction and magnitude of the electric field on charge q due to uniform electric
filed?
c.
On the diagram below draw and label all the applied forces on charge q.
d. Calculate the angle ϴ between the wall and the string.
e. Calculate the shortest distance between the wall and charged sphere.
f.
The string is cut:
i.
Calculate the magnitude of the net acceleration of the charged
sphere q.
ii.
Describe the resulting path of the charged sphere.
23
5. Two small spheres with masses m 1 = m2 = m = 25 g are hung by two silk threads of length L = 1.8
m from a common point. The spheres are charged with equal charges q1 = q2 = q, each thread
makes an angle ϴ = 25 ̊ with the vertical line.
a. On the diagram below draw and label all the applied forces on each sphere.
b. Calculate the distance between the spheres.
c.
Calculate the magnitude of the electric force between the spheres.
d. Calculate the magnitude of the charge on spheres.
Some of the electric charge has left the spheres due to humidity in the room. Assuming the electric
charge leaves the spheres at the same rate and after some time the new angle between the string and
the vertical line is 10 ̊.
e. Calculate the change in the electric charge on each sphere when the angle changes from 25 ̊
to 10 ̊.
24
Answers for Multiple Choice:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
A
B
C
B
A
C
A
D
C
B
A
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
C
B
D
C
B
C
D
C
D
D
D
C
B
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
C
B
D
B
C
A
D
C
B,D
B,C
B,D
B,C
Answers
1.
The plastic rod becomes negative,
and the fur becomes positive (the
magnitude of each charge is the
same).
2.
Two. Positive and negative.
3.
Bring them near a neutral object, and
see if they attract the new object by
inducing an opposite charge in it. The
magnitude of the charge on each
object is the same, and it is of
opposite sign.
11.
No. The smallest free charge has a
magnitude of “e.”
12.
Eight.
13.
Positive. Ion.
14.
The glass loses electrons. Protons
are too massive too move, they are
physically deep within the nucleus.
Only electrons move.
15.
4.
They repel each other.
5.
They attract each other.
6.
They repel each other.
7.
Benjamin Franklin.
8.
Proton. Electron.
9.
Negative. Ion.
10.
Empty space.
Conduction via a positively charged
rod, or Induction via a negatively
charged rod and a ground.
16. Place the charged rod near the top of a
grounded electroscope. Remove the
ground with the rod still there. Electrons
will move up the ground wire from the
Earth to the Electroscope. When the
ground wire is removed, the electrons
remain behind on the Electroscope for a
net negative charge.
17. The bits of paper will be attracted since
the negatively charged rod will locally
polarize the paper, pushing its electrons
further from the surface, leaving behind
a positive charge which is attracted to
the rod. .
25
18. Electrons are moving between the
sweater and the shirt due to friction.
This is evidenced by sparks.
19. The metal ball is insulated from ground,
so the positively charged rod attracts
electrons from the far side of the sphere
to the near side, and then the ball is
attracted to the rod.
20. Negative. The rod repels more negative
charges from the top of the
Electroscope to the leaves, forcing them
apart further.
21. Put a positive rod near each paper slip,
without touching. If one repels, then it
has a positive charge. If both are
attracted, then the test is inconclusive.
Take a negative rod and then the paper
that is repelled has a negative charge.
The neutral paper is attracted to both
negative and positive rods.
28. No.
29. An Electric Field is a field of Electric force
surrounding a charged particle. It is defined
from Coulomb’s Law by dividing out of the
equation a small positive test charge. The
force on another charged particle in the
field is then calculated by multiplying the
value of the charge by the Electric Field.
30. If they did, then different values of Electric
force (direction and/or magnitude since the
Electric Force and Field are vectors) would
be calculated at the same physical position,
and this is impossible. Electric Field lines do
not exist – they are used to help picture the
forces due to the charge.
31.
22. This is charging by induction. Negative.
23. Yes. Electric force does not require a
physical medium.
24. Decreases by a factor of four.
25. Electric force is very much greater than
gravitational force.
If there was a negative charge, the
Electric Field lines would point inwards –
towards the charge.
26. 3F0
27. Both depend on the inverse square of
the distance between the
masses/charges. Gravity is always
attractive. Electric Force is attractive or
repulsive, and is much stronger than
gravity.
32. The more lines per unit area (or volume)
indicate a stronger Electric Field. A stronger
Electric Field is also indicated by longer
Electric Field lines.
26
33. Both fields decrease in strength as 1/ r2 and
are described by similar mathematical
equations. The Gravitational Field is much
weaker than the Electric Field. The
Gravitational Field always provides an
attractive force, where the Electric Field
provides either an attractive or repulsive
force depending on the signs of the charges
involved.
34. The Electric Field.
35. The Electric Field due to each charge is
calculated independently, and then they are
vectorially added to find the total field at
the point.
Chapter Problems
1.
2.
3.
4.
900 N, repulsive
1.3x10-1 N, attract
7.7mC, positive
-8.0 x 10-8 C,
5.0 x 1011 electrons
5.
6.
7.
8.
9.
10.
11.
12.
6.36 x 10-5 N, repulsive
3.24 N, repulsive
4.4 m
12 m
2.7 x 10-7 C, positive
-1.27 x 10-7 C, 7.95 x 1011 electrons
2.0x10-3 N repulsive
kqeqe /Gmeme =4.2x1042
1.25 x 103 N/C
3.15 N
1.3 x 103 N/C
1.1 x 103 N/C toward the negative charge
1.0 x 10-6 C
4.8 x 103 N/C away from the positive
charge
19. 2.3 x 10-6 C
20. FG = 1.29 x 10-34 N
FE = 1.60 x 102 N; FE >> FG
25. 1.58 N/C
26.
27.
13.
14.
15.
16.
17.
18.
28.
21. FG = 3.21 x 10-48 N
FE = 1.34 x 10-5 N; FE >> FG
22. 5.58 x 10-11 N/C
23. FG = 1.03 x 10-35 N
FE = 1.28 x 101 N; FE >> FG
24. FG = 6.20 x 10-49 N
FE = 2.58 x 10-6 N; FE >> FG
27
29.
32. a. 2.6 x 103 N/C to the right
b. 7.9 x 102 N/C to the left
c. 1.8 x 103 N/C to the right
33. a. 1.7 x 104 N/C to the right
b. 9.7 x 103 N/C to the right
c. 2.3 x 102 N/C to the left
30.
d. 2.7 x 104 N/C to the right
34. a. 8.1 x 103 N/C to the left
b. 7.0 x 102 N/C to the left
c. 8.8 x 103 N/C to the left
35. a. 1.2 x 104 N/C to the right
b. 5.5 x 103 N/C to the right
c. 4.6 x 102 N/C to the right
31.
d. 1.8 x 104 N/C to the right
28
Free-Response
1. a. To the right
b. 1.5 x 105 N/C
c. To the right
d. 0.15 N
e. 60 m/s2
4. a. To the left
2. a. Down
b. 2.8 x 105 N/C
c.
d. 1.25 x 10 -7 C; the sign should be
negative
b. 0.045 N
c.
d. 𝜃 = 24.7O
e. r = 0.25 m
f. i. 10.8 m/s2
ii.
3. a. 1.8 x 104 N/C
b. 1.8 x 104 N/C
c.
5. a.
d. 2.5 x 104 N/C
b. 1.52 m
c. 0.114 N
d. 5.4 x 10-4 C
e. 4.2 𝜇C
29